29:null 2a:["$","title",null,{"children":"Ramanujan's Infinite Series for π | Herb Susmann | Observable"}] 2f:[] 2d:{"id":"42d846335acbf063","slug":"ramanujans-infinite-series-for","title":"Ramanujan's Infinite Series for π","thumbnail":"75e33219f49cdca3d5f919a6dae9d6d4ed9fdc741e45c91155f98ed22bbeb45a","access_level":"public","create_time":"$D2021-08-10T13:37:53.420Z","update_time":"$D2021-08-10T14:25:47.329Z","view_time":null,"first_public_time":"$D2021-08-10T14:25:29.116Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"a848bf10c248efb2","login":"herbps10","name":"Herb Susmann","avatar_url":"https://avatars-next.observableusercontent.com/3d8000aa2ff6515179603ce3451b0104272bd8b602dd87bb09f033573d6fa6a5","tier":"starter_2024"},"version":220,"publish_version":220,"role":null,"authored":false,"authors":[{"type":"individual","id":"069af68ad7bd402a","login":"herbps10","name":"Herb Susmann","avatar_url":"https://avatars-next.observableusercontent.com/3d8000aa2ff6515179603ce3451b0104272bd8b602dd87bb09f033573d6fa6a5","tier":null}],"members":[{"type":"individual","id":"069af68ad7bd402a","login":"herbps10","name":"Herb Susmann","avatar_url":"https://avatars-next.observableusercontent.com/3d8000aa2ff6515179603ce3451b0104272bd8b602dd87bb09f033573d6fa6a5","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Ramanujan's Infinite Series for π","cells":[{"id":0,"value":"# Ramanujan's Infinite Series for π\nInfinite series for π owed to [Srinivasa_Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Mathematical_achievements) that converges rapidly.\n${tex.block`\n\\frac{1}{\\pi} = \\frac{2\\sqrt{2}}{9801} \\sum_{k=0}^{\\infty} \\frac{(4k)!(1103 + 26390k)}{(k!)^4 396^{4k}}\n`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"html`\n\n \n\n\n ${results.map((result) => {\n return html`\n \n \n \n `;\n })}\n\n

Terms	Estimate of ${tex`\\pi`}
${result.i}	${highlightCorrect(result.pi.toString().substring(0, 55), pi)}

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"results = series(7).map((x, i) => ({ \n i: i + 1, \n pi: (new BigNumber('1')).dividedBy(x),\n}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":158,"value":"highlightCorrect = (estimate, truth) => {\n let i = 0;\n while(estimate.substring(0, i) == truth.substring(0, i) && i < truth.length) i++;\n\n const correctPart = estimate.substring(0, i - 1);\n const incorrectPart = estimate.substring(i - 1);\n return html`${correctPart}${incorrectPart}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":148,"value":"pi = '3.14159265358979323846264338327950288419716939937510'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"series = function(K) {\n BigNumber.set({ DECIMAL_PLACES: 100, ROUNDING_MODE: 4 })\n\n const mult = new BigNumber('2').times((new BigNumber('2')).sqrt()).dividedBy(new BigNumber('9801'));\n let sums = [new BigNumber(0)];\n for(let k = 0; k < K; k++) {\n let kBig = new BigNumber(k);\n sums[k + 1] = sums[k].plus(mult.times((factorial(kBig.times(4)).times(kBig.times('26390').plus('1103'))).dividedBy(factorial(k).pow(4).times((new BigNumber('396').pow(kBig.times('4')))))));\n }\n sums.splice(0, 1);\n return sums;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":27,"value":"factorial = function(n) {\n var total = new BigNumber(\"1\");\n for(let i = 0; i < n; i++) {\n total = total.times(new BigNumber(n - i));\n }\n return total;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":96,"value":"BigNumber = require('bignumber.js@9.0.1/bignumber.js')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2e:"$2d:body"